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Abstract
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear inputplantoutput systems to arbitrary quantum nonlinear Markovian inputoutput models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the inputoutput relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entries that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arise algebraically as Schur complements and amounts to a model reduction where the fast degrees of freedom are decoupled from the slow ones and eliminated.
Original language  English 

Article number  013506 
Journal  Journal of Mathematical Physics 
Volume  56 
Issue number  013506 
Early online date  20 Jan 2015 
DOIs  
Publication status  Published  Jan 2015 
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Dive into the research topics of 'Characteristic operator functions for quantum inputplantoutput models and coherent control'. Together they form a unique fingerprint.Projects
 1 Finished

Quantum Stochastic Analysis for Nanophotonic Circuit Design
Gough, J. (PI)
Engineering and Physical Sciences Research Council
01 Aug 2013 → 31 Mar 2015
Project: Externally funded research